A Short Course in Ordinary Differential Equations

1. Front Matter

   Pages i-xii

   PDF

2. Initial Value Problems

   • Qingkai Kong

   Pages 1-29

3. Linear Differential Equations

   • Qingkai Kong

   Pages 31-60

4. Lyapunov Stability Theory

   • Qingkai Kong

   Pages 61-100

5. Dynamical Systems and Planar Autonomous Equations

   • Qingkai Kong

   Pages 101-166

6. Introduction to Bifurcation Theory

   • Qingkai Kong

   Pages 167-201

7. Second-Order Linear Equations

   • Qingkai Kong

   Pages 203-250

8. Back Matter

   Pages 251-267

   PDF

This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm—Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for seniorundergraduates as well.

• Lyapunov function method
• Poincaré-Bendixson theorem
• Sturm–Liouville problems
• bifurcation theory
• linear differential equations
• stability theory
• ordinary differential equations

“All material is carefully organized and presented in a transparent manner. The text contains a large number of solved problems which illustrate well theoretical material. Each chapter concludes with a selection of exercises for independent study; hints and answers to exercises are collected in the end of the book along with a useful list of references and a subject index. … Undoubtedly, this book is a very valuable contribution to existing texts on qualitative theory of differential equations.” (Yuriy V. Rogovchenko, zbMATH, Vol. 1326.34007, 2016)

• Department of Mathematical Sciences, Northern Illinois University, DeKalb, USA

  Qingkai Kong

Qingkai Kong is a Professor and Director of Undergraduate Studies in the Department of Mathematical Sciences at Northern Illinois University. He holds a M.Sc and Ph.D from the University of Alberta. Dr. Kong is a recipient of the Huo Ying-Dong Teaching Award and has refereed for over 50 journals.

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